pymgarch

Multivariate GARCH for Python: DCC, ADCC, and CCC correlation dynamics built on top of arch univariate marginals, validated against R's rmgarch/tsmarch.

Why

Python has no maintained general-purpose multivariate GARCH framework. The existing packages cover Gaussian DCC(1,1) at most, while R users have had DCC, ADCC, GO-GARCH and copula-GARCH in rmgarch (now tsmarch) for a decade. pymgarch closes that gap incrementally, starting with the correlation layer:

• stage 1 (univariate volatility) is delegated to arch, the ecosystem's dominant, battle-tested GARCH package;
• stage 2 (correlation dynamics) is what this library implements, with correct two-stage Engle-Sheppard standard errors and replication tests against rmgarch's fitted parameters and likelihoods.

Install

pip install pymgarch          # or: pip install pymgarch[numba]

The optional numba extra JIT-compiles the correlation recursions; without it everything runs in pure NumPy.

Quickstart

import pymgarch as mg

# returns: (T, N) DataFrame, percent scale recommended
res = mg.DCC(dist="t").fit(returns)
print(res.summary())

res.conditional_correlations   # (T, N, N)
res.conditional_covariances    # (T, N, N)

fc = res.forecast(horizon=10)                    # analytic
fc = res.forecast(horizon=10, method="simulation", n_paths=2000)
flt = res.filter(new_returns)                    # fixed params, new data

Marginals default to constant-mean GARCH(1,1). Customize per-column via a spec, or bring your own fitted arch results:

spec = mg.UnivariateSpec(vol="GARCH", p=1, o=1, q=1, dist="t")  # GJR-t
res = mg.ADCC().fit(returns, marginals=spec)

from arch import arch_model
fitted = [arch_model(returns[c], rescale=False).fit(disp="off") for c in returns]
res = mg.DCC().fit(returns, marginals=fitted)

Models (v0.1)

For large cross-sections, DCC and ADCC accept method="composite" (Engle- Shephard-Sheppard pairwise composite likelihood), replacing the N-dimensional likelihood with O(N) bivariate recursions for the default contiguous pairs (O(N^2) with pairs="all").

Standard errors: the correlation-family models (DCC/ADCC/copula) use Engle-Sheppard (2001) two-stage sandwich estimates -- marginal and correlation scores stacked so stage-2 uncertainty reflects stage-1 estimation error, with correlation targets held fixed (the same approximation rmgarch makes); if the stacked system is singular the library falls back to a stage-2-only sandwich and says so in summary(). Composite fits report Godambe-sandwich SEs labelled composite-godambe. BEKK is estimated in a single stage, so its SEs are a plain QML sandwich (qml-robust) that additionally holds the estimated mean and targeting covariance fixed; on boundary or degenerate optima it degrades to NaN SEs with a warning instead of failing the fit.

License

MIT